Reliable Navigation of Mobile Sensors in WirelessSensor Networks without Localization Service

Qingjun Xiao, Bin Xiao, Jiaqing Luo and Guobin LiuDepartment of Computing

The Hong Kong Polytechnic UniversityHunghom, Kowloon, Hong Kong

E-mail: {csqjxiao, csbxiao, csjluo, csgliu}@comp.polyu.edu.hk

Abstract—This paper deals with the problem of guiding mobilesensors (or robots) to a phenomenon across a region covered bystatic sensors. We present a distributed, reliable and energy-efficient algorithm to construct a smoothed moving trajectoryfor a mobile robot. The reliable trajectory is realized by firstconstructing among static sensors a distributed hop count basedartificial potential field (DH-APF) with only one local minimumnear the phenomenon, and then navigating the robot to thatminimum by an attractive force following the reversed gradientof the constructed field. Besides the attractive force towardsthe phenomenon, our algorithm adopts an additional repulsiveforce to push the robot away from obstacles, exploiting the fastsensing devices carried by the robot. Compared with previousnavigation algorithms that guide the robot along a planned path,our algorithm can (1) tolerate the potential deviation from aplanned path, since the DH-APF covers the entire deploymentregion; (2) mitigate the trajectory oscillation problem; (3) avoidthe potential collision with obstacles; (4) save the preciousenergy of static sensors by configuring a large moving stepsize, which is not possible for algorithms neglecting the issueof navigation reliability. Our theoretical analysis of the abovefeatures considers practical sensor network issues including radioirregularity, packet loss and radio conflict. We implement theproposed algorithm over TinyOS and test its performance onthe simulation platform with a high fidelity provided by TOSSIMand Tython. Simulation results verify the reliability and energyefficiency of the proposed mobile sensor navigation algorithm.

Index Terms—Hybrid Sensor Networks, Mobile Sensors Nav-igation, Location Free, Angle of Arrival, Navigation Reliability.

I. INTRODUCTION

Hybrid sensor networks comprising of mobile sensors andcheap static sensors open new frontiers in a variety of militaryand civilian applications. In hybrid sensor networks, a largequantity of networked static sensors monitor the environment,while a few mobile sensors provide the actuation with lo-comotion modules equipped. Typical usages of these mobilenodes include energy recharge for static sensors, collectionof a large volume of data in Delay Tolerant Networks, coun-terattack against intruders. As a summary, the emergence ofhybrid sensor networks converts the static sensor networks forenvironmental monitoring into a reactive or active system [1].

One fundamental problem for the hybrid sensor networks ishow to guide a mobile sensor to a phenomenon across the re-gion covered by static sensors while evading the obstacles [1].This problem is different from the past robot path planning

problem based on centrally stored map, since the mobilesensors (or robots) utilize distributed sensing ability of staticsensors to detect dangers (or obstacles) and their distributedcomputations plus wireless connections to plan the movingtrajectories collaboratively. These distributed sensing and pathplanning abilities can enhance the robots’ ability to functionin unfamiliar environments, where the hybrid sensor networkshas two advantages: easy-to-deploy (e.g., by a flying vehicles)and more accurate sensing ability. For example, within a forest,their distributed sensing abilities can penetrate through thethick vegetation to detect wild fire early, and in a battlefield, they can not be easily deceived by enemies’ disguise,if compared with the remote sensing based on satellites.

For the problem of mobile sensor navigation assisted bystatic sensors, one constraint is that an effective localizationservice for static sensors is not always available, especially incomplex concave regions [2], [3]. Moreover, localization ser-vices may require additional ranging hardware that increasesWSNs deployment cost, and running localization services mayelongate the network deployment time, consumes the preciousenergy of static sensors. Considering these facts, we have thislocation-free assumption, which may invalidate some previousmobile sensor navigation schemes. For example, the Berkeleysolution [4] of the pursuer-evader game depends on the staticsensors with location knowledge to track the evader and guidethe pursuer to the reported position by an installed map, whichhowever may be unavailable in unfamiliar environments.

Several recent works [1], [5] can remove these location andmap assumptions by running a location-free routing protocolwithin the network and by navigating the robots following therouting path to the sensor detecting the phenomenon. To makethe routing path more tangible for robots, a navigation bandis explicitly built by [5] along the path and the robot knowsits relative position to the band by wireless communications.However, there are two inadequacies for these previous works.First, the robots are only guided by networks and the readingsfrom sensors carried by the robots are forgotten, which canprovide fast response to unexpected obstacles. Second, theguiding from networks depends on wireless communications,which are by nature unreliable (e.g., radio irregularity, lossychannels and radio conflicts). It’s not yet clear how this com-munication unreliability affects the robots’ navigation quality.

This paper mainly provides two contributions for this prob-

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lem of location-free robot navigation. First, through bothanalysis and simulation studies, we demonstrate that, for thenavigation based on unreliable talks with the static sensornetworks, the robots frequently make wrong decisions abouttheir next step moving directions. The robots therefore maycollide with obstacles, deviate from an planned path or moveout of sensor deployment fields, which reduces the navigationqualities and consumes their energies. Moreover, the robotsmay suffer from path oscillation, caused by the narrownessof the navigation band. Second, we present a reliable robotnavigation algorithm which can handle the unreliability inwireless communications, construct a smoothed robot movingtrajectory and improve the reliability of robot navigation. Ouralgorithm is based on the artificial potential field (APF) [6]and adopts a two layer architecture [7] - a global path planningmodule over a local obstacle avoidance layer. The globalplaning is conducted by an event dissemination initiated bythe static sensor detection an phenomenon. This disseminationconstructs a distributed hop count based APF (DH-APF),which has only one local minimum near the phenomenon.Afterwards, the reversed gradients of this DH-APF can provideto the robots attractive forces leading them to the phenomenon.In practice, we propose to implement these attractive forces byan elegant integration of the robot navigation protocol and thetree based routing protocol with the pull rule. Additionally, theagile repulsive forces can be provided by the fast readings fromthe robots’ sensors to steer the robots away from unexpectedobstacles (called reactive local obstacle avoidance).

Our algorithm is different from the previous works [1], [8]–[10] that also deal with navigation qualities for the followingreasons. (1) Their major quality metric is the exposure todanger problem, since they models the navigating robots eitheras malicious entities trying to avoid the tracking by staticsensor networks or as cautious entities trying to keep thesafest distance to obstacles. In contrast, our work regards thatthe duty of sensor networks is only to provide optimizednavigation guidance to the goals and without the collisionwith obstacles, and that the obstacle avoidance should be theduty of robots themselves by their self-carried sensors. Inthis way, the static sensors can save the energy for dissem-inating the knowledge about obstacles and robots make theirown decisions on avoiding obstacles (perhaps fast movingunexpected ones), since no matter how fast the wirelesscommunications are in spreading out obstacles’ knowledge,they can not compete with the speed of robots’ self-carriedsensors. (2) Their navigation quality evaluation is conductedassuming ideal sensor communication model. Although [1]also presents the imperfect radio channel problem, it doesnot present systematical analysis on how error-prone natureof sensor networks affects robots’ navigation quality, whichis one of the major focuses of this paper. (3) Previous worksfails to consider the trajectory smoothness, which is one of theadvantages of our algorithms, since we recommend to smooththe attractive forces of all upstream nodes rather than to followthe direction of only one upstream node on the planned path.

To verify the designed features of our navigation algorithm,

we implement the behavior of static sensors over TinyOS [11]and the functions of mobile sensors by Tython [12]. Thenwe evaluate the performance of our algorithm in a controlledenvironment provided by TOSSIM [13], which can simulateirregular radio propagation, radio conflict and lossy networkbehavior at a high fidelity by its empirical probability biterror model. Based on this prototype system and simulationplatform, we evaluate the path quality, which shows theeffectiveness of our algorithm in producing smoothed path, intolerating collision with obstacles and in reducing the chancesof out-of-field and path oscillation.

The rest of the paper is organized as follows. In sectionII, we highlight the related work and introduce a two layerarchitecture for path planning. In section III, we formulatethe location-free robot navigation problem and explain aninspiring scenario used throughout the paper. Section IV andV separately present the planning part and the navigation partof our two layer algorithm. Section VI shows the simulationresults and section VII concludes our work.

II. RELATED WORK

Path planning is an extensively studied topic in the field ofrobot motion planning. Proposed algorithms can be broadlygrouped into two categories [14]: local and global approaches.Local planning considers only local information about thesurrounding, obtained from the sensors carried by robots(e.g., APF [6], VFH+). Global planning is based on theglobal knowledge of the workspace (e.g., Wavefront [15],A*, roadmap). Generally speaking, local approaches supportreal time response to obstacles, but are impossible to achieveoptimal trajectories and suspectable to trap in local minima.The global approaches can produce optimal and smoothedtrajectory, but with slow response to environmental changes.

In the field of traditional robot motion planning, the two-level robot navigation structure (Fig. 1) is a widely-acceptedarchitecture [14]: a global trajectory is calculated in the globalplanning phase, while in the local obstacle avoidance phase therobot reads its own sensory data and adjusts the local trajectoryin a reactive way, which gives the robot the ability to cope withunexpected obstacles. This division into two layers is primarilydue to the high computation and communication cost requiredin most global planning techniques.

Feedback

Task

Global Path orNavigational Field

Local Path

Two Layer Robot Navigation Architecture

Maps or Net-worked Sensors Path Planning

Self-carriedSensors Local Obstacle Avoidance

Robot & Environment Motor Control

Fig. 1. A two-layer robots navigation system.

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The traditional two level architecture needs to be adjusted inthe background of hybrid sensor networks, since it is the staticsensor network, rather than a map, who gives robots the globalknowledge about the whole region and plans the global pathaccordingly. Compared with the dead maps, the networkedstatic sensors can sketch a real-time picture of the unfamiliarenvironments. This navigation scheme by sensor networks hasbeen adopted by a recent work [5], which however forget aboutthe self carried sensors in the Local Obstacle Avoidance layer.

Another adaptation to the traditional architecture in Fig. 1is to change the data coupling between the two layers. Thetraditional coupling by Global Path may be unsuitable in hy-brid sensor networks, since whenever the old path invalidates(e.g., robots deviate from the old path), a new path shouldbe reconstructed, which is more feasible on a centralized mapthan within a distributed sensor network due to different costof path reconstruction. A more appropriate coupling is bya Navigational Field covering the entire sensor deploymentregion, for the following reasons. First, the frequency for therouting path to be invalid can be high in sensor networks,because (1) the routing path is by nature zigzag and mayintersects with obstacles, and (2) it can be difficult to controlthe robots to navigate strictly along the routing path, since thiscontrol is implemented via irregular and error-prone wirelesscommunications. Second, a navigational field covering theentire deployment region can give the local obstacle avoidancelayer more freedom to steer the robots and avoid unexpectedobstacles without the inhibitive cost of recomputing the globalpath. This freedom is important, since the reliability of navi-gation assisted by sensor networks can be much lower due tothe unreliability of wireless channels.

III. PROBLEM FORMULATION

A hybrid sensor network comprises of numerous static sen-sors and a few mobile sensors, with three major assumptions.(1) Different from the static sensors, the mobile sensors canchange their geometric locations autonomously. For the sakeof simplicity, their mobility platforms are assumed to be free-flying, which explains why the robots can be treated as points.This assumption in future can be relaxed to be holonomic ornonholonomic mobility platform. (2) Although the nodes havedifferent mobilities, their wireless communication componentsare homogeneous, i.e. the same MAC protocol over the sametype of radio antennas configured to the same power level. Inour experiments, the adopted wireless module is the TinyOSactive message layer [11] over a CC2420 RF transceiver.(3) Robots are assumed to be able to detect the Angle-of-Arrival (AoA) of incoming radio signals, by amplitudeanisotropy or phase interferometry. Radio AoA devices arerecognized to be too expensive to deploy on the massivestatic sensors, but they’re affordable to equip on a few robots.Fig. 2(a) illustrates such a hybrid sensor network with a gridarrangement of a ten feet spacing (the simulation sectionpresents other network configurations, like random sensordistribution and sparse networks). The exemplified networkhas only one mobile sensor located at the left bottom corner.

Mobilesensor

Fire

Impassable region • •with high temperature

• •Event •owner

Ideal Path

(a) The mission and the ideal path

Planned Path

Moving Trajectory

(b) Our trajectory and routing path.

Fig. 2. A rescue mission carried by a hybrid network in an on-fire building.

For a mobile sensor, its free moving space is not theentire region covered by the network, due to the existence ofobstacles. The static sensors know the presence of obstaclesin their own vicinities, by checking their ADC readings. Inour scenario, the obstacles are regions with high temperature,which may paralyze the function of a mobile sensor. A staticsensor can measure the temperature and tell whether it’ssafe for robots by comparing its reading with a predefinedthreshold. Fig. 2(a) has only one obstacle colored by red,where the temperatures are above a threshold of 100◦C.

When an event of interest occurs within the network, staticsensors can detect its occurrence and forward this messageto robots by some protocol. Mobile sensors then navigate tothe phenomenon region to provide actuation, which is thebasic motivation of hybrid sensor networks. This complex con-ceptual process includes event detection, event identification,event notification and robot navigation. Event detection andidentification are application specific issues and beyond thescope of this paper. For simplicity, we assume only one staticsensor is the owner of an event, whom is probably chosen bya small scale leader election held in the phenomenon region.

The objective of this paper is to design effective algorithms(1) for the static sensors to collaboratively conduct path plan-ning during the event notification phase initiated by the eventowner, and afterwards (2) for the mobile sensor to develop asense of direction and navigate accordingly, until it establishesa direct radio link with the event owner. The constraints for thispath planning and robot navigation problem include: (1) finalnavigation path for the robot should be collision-free for itssafety; (2) static sensors do not know their geometric locations;(3) the radio model for sensors, both static and mobile, is notunit disk based but follows the empirical probabilistic bit errormodel in TOSSIM, which permits irregular radio propagation,packet loss and radio conflicts. Although the above problemdefinition includes only one event owner and one robot, it canbe easily extended to multiple owners and multiple robots, byincorporating the semantics of Anycast.

The following two sections present a reliable solution forthis navigation problem in wireless sensor networks, compris-ing of two consecutive phases: a path planning phase followedby a robot navigation phase. The planning phase correspondsto the Path Planning layer in Fig. 1 and is discussed inSection IV. The navigation phase relates to the Local Obstacle

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Avoidance layer and is explained in Section V.

IV. PATH PLANNING PHASE

The path planning phase is a process initiated by theevent owner to search for a path to the robot and notifythe robot about the occurrence of a certain event. But whenthis phase completes, not a single path but a distributed hopcount based artificial potential field (DH-APF) is established,which is essentially a distributed scalar field with only oneglobal minimum at the event owner. The gradients of DH-APF thus, in the subsequent navigation phase, can help therobot develop a sense of direction and navigate to the eventowner. This section firstly presents a distributed DH-APFconstruction algorithm called distributed wavefront and lateridentifies several innate inadequacies of this DH-APF, whichinspire us to design a reliable robot navigation algorithm inSection V.

A. Distributed Wavefront Algorithm

The design space for the path planning phase is extremelynarrowed by two constraints: distributed computing and lo-cation free. The decentralization requirement inhibits the useof centralized search algorithms (e.g., A*), since their coordi-nation among different search branches can incur unbearablyhigh communication cost. The absence of location knowledgebans the use of heuristic search algorithms inspired by thegeometric location (e.g., various geometric routing algorithms,GHT, double ruling). The wavefront algorithm [15] howevercan satisfy these two requirements, which is essentially abreadth first path search algorithm resembling the well-knownflooding in the field of network routing. A wave is initiated byan event owner and gets propagated among networked staticsensors, by which we are able to construct a DH-APF withonly one local minimum.

We present a rule-based description of a distributed wave-front algorithm in TABLE I, which is deployed on all staticsensors. A typical execution of the rule-based code is asfollows. The event occurrence triggers the execution of Initiaterule on the sensor who is the event owner. The owner thensends to itself a loop-back message with hopcount −1, whichactivates the Push rule on the owner. The Push rule updatesthe hopcount of the owner as 0 and propagates that numberto its neighborhood by rule Propagate. Upon the receivingof hopcount 0 from the owner, the neighbors of the ownerschedule the execution of their Push rules. The process repeatsand it terminates when the hopcounts of all static sensorsare configured to their proper values (see the Ignore rule).However, the sensors in impassable regions is excluded fromthe above DH-APF construction process, since sensors thereby applying the Impassable rule disable all their activities.But we do not assume that our static sensors in impassableregions with high temperature in the scenario can endure theheat there, because (1) sensors that are destroyed by the heatcan not involve in the DH-APF construction, and (2) sensorsstill alive voluntarily exclude themselves from the process andpretend to be destroyed.

TABLE IDISTRIBUTED WAVEFRONT ALGORITHM FOR STATIC SENSORS

# state definitions for a static sensor

integer hopcount := INFINITY. # my hopcount

# ‘defrule’ marks the beginning of a definition, while ’.’ tells the end.

# ‘:’ separates definition name and body.

# ‘⇒’ is a mapping from condition to a sequence of actions.

# ‘;’ indicates a sequential execution between two actions.

# bold letters emphasize events or actions that can signal events.

# rule definitions for a static sensor

defrule Impassable : # if impassable, it shields all rules that follows

my vicinity is not suitable for passage ⇒ do nothing.

defrule Initiate :

become an event owner ⇒ send −1 hopcount to myself.

defrule Ignore :

receive a hopcount no more than one hop different from mine

⇒ do nothing.

defrule Push :

receive a hopcount at least two hops smaller than mine ⇒update my hopcount as the received hopcount plus one;

activate rule Propagate.

defrule Propagate :

choose a backoff (half of window plus jitter);

send my hopcount to vicinity;

choose a backoff (half of window plus jitter);

resend my hopcount to vicinity. # increase comm reliability

B. Algorithm Evaluation and Enhancement

The distributed wavefront algorithm establishes a DH-APFcovering the obstacle-free region and with a global minimumat the event owner. One such field is shown by Fig. 3(a),in which the three LEDs of each sensor display the lowestthree bits of that sensor’s hopcount and each gray arrowoutgoing from a sensor indicates from which neighbor thatsensor updates its hopcount to the current value. However,the DH-APF established by networked static sensors is farfrom the ideal APF constructed from map, according to ourexperiments. We identify several problems of DH-APF: (1)Zigzag Planned Path; (2) Link �= Safe - the possibility thatradio links intersect with obstacles; (3) Backward Link; (4)Coverage problem - flooding fails to cover all sensors andthe robot may fail to hear about the flooded event. Althoughthese problems are largely inevitable due to the unreliabilityof wireless links and the sparse distribution of static sensors,we recommend an enhancement by the Pull rule to mitigateproblem (3)&(4) at the end of this subsection.

The Zigzag Planned Path problem is due to the much lowerresolution of sensor distribution than grids in a map and themuch longer connectivity range of sensors than the distancebetween neighboring map grids. Traditionally, the strengthof globally planned path based on maps is its promise to(1) generate optimized global pathes, (2) avoid trap in localminima and (3) construct smoothed pathes. When the planningis changed to be conducted by sensor networks, the advantages

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Fail to receive flooding

Backward link

Zigzag path

(a) Distributed wavefront.

Zigzag path

Link = Safe?

(b) Distributed wavefront with pull.

Fig. 3. The enhancement to the generation of DH-APF by the pull rule.

(1) and (2) are partially retained but the third one is sacrificedthat will lead to a Zigzag planned path. This low quality zigzagpath is one of the reasons that we are reluctant to restrict therobots to navigate along the path planned by sensor networks.

The Link �= Safe problem may mislead the robots to collidewith obstacles, if they follows those dangerous links. It is afundamental assumption beneath grid based motion planningalgorithms [14], that the link connecting two neighboring gridslies in free space if the two grids are in free space. Thisassumption however may not hold for the sensor networksif we simply regard static sensors as grids. This link �=Safe problem is one of the proofs that navigation guided bystatic sensors may not be collision-free and reliable obstacleavoidance assisted by robot sensor readings is necessary.

The Backward Link is a well-known problem of the span-ning tree built from flooding, which can potentially misleada robot to move to a wrong direction. We recommend anadditional Pull rule (see TABLE II) to reduce the possibilityof backward links. When the end node of a backward linkpropagate its own hopcount by Push rule, some neighbormay detect the existence of the backward link, by findingthe propagated hopcount is at least two hop larger than theone owned by itself. The detector then correct the backwardlink by propagating its hopcount and making the end nodeof the backward link point to itself. The effectiveness of thePull rule to reduce backward links is illustrated in Fig. 3(b).Another use of the Pull rule is in Section V for the robotto query its neighbors for their hopcount. When the robotbroadcasts a hopcount with value INFINITY, the Pull ruleof its neighboring sensors will be activated to schedule apropagation of their own hopcounts in near future.

The Coverage problem, similar to the Backward Link prob-lem, is caused by fault-prone radio links. This problem of howto disseminate events reliably to robots has already been solvedby adopting the eventual consistency semantics in Trickle[16], which in fact also adopts the Pull rule. As a summary,the Pull rule is a MUST for three reasons: reliable eventdissemination, backward links mitigation and neighborhoodquerying by robots. The additional energy consumption byadopting the Pull rule is inevitable.

TABLE IIADDING THE PULL RULE

defrule Pull : # increase the chance of propagation of smaller hopcount

receive a hopcount at least two hops larger than mine ⇒activate rule Propagate.

V. ROBOT NAVIGATION PHASE

For the robot navigation phase, we present an algorithm togive the robots a sense of direction based on the reversedgradients of DH-APF, which are calculated by only localcommunications between an robot and its immediate neigh-bors. Here, we assume the presence of radio AoA devices onrobots to eliminate the need for location knowledge of theneighbors. However, we argue that robot navigation purely byreversed gradients is unsafe and it should be combined withthe agile sensing ability of the robot’s sensors. Additionally,we compare the performance of navigation field with that ofnavigation band [5] and show the effectiveness of navigationalfields in tolerating deviation and mitigating oscillations.

A. Robot Navigation guided by Reversed Field Gradients

The purpose of this navigation phase is to generate acollision-free moving trajectory starting from the robot’s initialposition and ending at a point within the one hop range of theevent owner. Fig. 2(b) illustrates one such trajectory in ourexemplified scenario where the planned path may pass througha dangerous area but the final moving trajectory of the robotremains to be safe. This navigation is a step-by-step processwith each step as a line segment. At the beginning of eachstep, the robot should determines this step’s moving directionby querying neighboring static sensors about their hop counts.The step size is an adjustable system parameter.

In TABLE III, we restate the above process without ambi-guity by a rule-based language. The activation of rule Start-Mission is a symbol of phase transition from Path Planningto Robot Navigation. The rule MissionDone is to terminatethis Robot Navigation phase. The rule MoveAStep, whichrecursively activates itself at the end, carries out the step-by-step navigation process. The third line of the MoveAStep ruleis a request to collect all hopcounts around the robot neigh-borhood by propagating an INFINITY hopcount to vicinity.The neighbors later respond with their hopcount applying thePull rule in TABLE II. The CollectGuide rule listens to andrecord critical information of these replies, based on whichwe estimate the reversed DH-APF gradient. In this algorithmdescription, the robot moves to its next position only followingthe direction of the estimated reversed DH-APF gradient. Thisnavigation based on reversed gradient can cause trouble, whichwe shall explain in the next subsection.

Here we describe the algorithm to calculate the reversedgradient −�∇f of the artificial potential field f(p) at the pointp0 = [x0, y0]T where robot locates. If f(p) is a continuousand differentiable scalar field, the required gradient caneasily be calculated by −�∇f |p0 = −∂f

∂p |p0 . However, theDH-APF constructed by static sensors is a discrete scalar

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TABLE IIIDISTRIBUTED WAVEFRONT ALGORITHM ON A ROBOT

# state definitions

import state hopcount defined for a static sensor.

bool onmission := FALSE.

list guides of struct <integer nbr, integer hopcount, double aoa >.

struct force < double dx, double dy >.

# rule definitions for a mobile sensor; here ’∧’ represents logical and

defrule StartMission :

onmission = FALSE ∧ my hopcount is updated ⇒onmission := TRUE;

wait still until flooding converges; # guides collection period

calculate the reversed DH-APF gradient �g from collected guides;

force := �g/|�g| · step size.

activate rule MoveAStep.

defrule MoveAStep :

move a step driven by the force;

stop the motor engine; clear the guides list;

hopcount := INFINITY; activate rule Propagate;

stay still for a period; # guides collection period

calculate the reversed DH-APF gradient �g from collected guides;

force := �g/|�g| · step size;

if onmission, then activate rule MoveAStep.

defrule MissionDone :

onmission = TRUE ∧ my hopcount is updated to one ⇒onmission := FALSE; stop the motor engine;

clear the guides list; hopcount := INFINITY.

defrule CollectGuide : # guides collection period

receive a hopcount from the neighor nbr with angle aoa ⇒if received hopcount is at least two hop smaller than mine,

then update my hopcount as the received hopcount plus one;

append <nbr, hopcount, aoa> to guides list.

import rule Propagate defined for a static sensor.

field and the knowledge collected by the robot includes onlyf(p0) : potential value at p0 or hopcount of the robotf(pi) : potential value at pi or hopcount of neighbor i−−→p0pi : unit vector from p0 to pi or the angle-of-arrival

of radio from neighbor i to the robot.Here the p0, pi, −−→p0pi are all defined in the robot’s localcoordinate frame, which do not need any translation into theglobal coordinate frame. The following is the equation toestimate the reversed gradient in the discrete scalar field builtby static sensors.

− �∇f |p0 =∑

f(pi)<f(p0)−−→p0pi +

∑f(pi)>f(p0)

−−→pip0 (1)

The mathematical meaning of Eq. (1) is the vector of leftderivative plus that of right derivative. Its physical meaningis that the upstream nodes (neighbors with hopcount smallerthan that of the robot) exert attractive forces on the robot, whilethe downstream nodes (with larger hopcount) exert repulsiveforces. The direction of the resultant force is treated as thereversed gradient direction. In Fig. 4, the reversed gradientdirection is calculated by combining the attractive force frommote 33 with hopcount 1 and the repulsive forces from motes

36 and 38 with hopcount 3. Although these forces directionare known from the robot radio AOA ability, robots do notneed to know their magnitude (all unified to one) with theabsence of range information.

Forces exerted on the robot by sensors with different hop counts

Resultant force for each step

Temperature readings

Mote id

MobileRobot

2hopsThis step

Previous step

Fig. 4. Deciding the moving direction by the reversed gradients of DH-APF.

B. Algorithm Evaluation and Enhancement

This subsection evaluates the performance of robot naviga-tion based on reversed gradients by both theoretical analysisand experiments. There are three potential problems in our al-gorithm (also existed in previous navigation algorithms guidedby static sensors): (1) possible deviation from planned pathes;(2) possible collision with obstacles; (3) oscillation in narrowpassages. After presenting these problems, we also recommendcorresponding solutions.

1) Error in reversed gradient estimation and its sources:It’s inevitable that an estimated reversed gradient deviatesfrom the real gradient, caused by many factors. For example,even in Fig. 5 where DH-APF is ideal, an obvious deviationcan happen between the real gradient �G and the estimatedreversed gradient �C. The �C is calculated by combining theattractive force �A from centroid of lower hopcount regionand the repulsive force �B from centroid of higher hopcountregion. It’s the deviation of �A and �B from �G that causes thedeviation of �C from �G. The deviation of �A and �B from �Gis due to the radio irregularity [17] of the robot. Therefore,the radio irregularity of robot is one of the reasons for errorin reversed gradient estimation. Other factors include theirregular DH-APF, instability in DH-APF (topology changes),nonuniform sensor distribution in robot’s neighborhood andmessage loss when the robot talks with its neighbors. With somany interfering factors, it’s difficult to predict and quantifythe error in the reversed gradient estimation.

RobotEventOwner

AG

CB

Fig. 5. Error in reversed gradient estimation with isotropic DH-APF.

An unexpected observation about the reversed gradientestimation is that it’s more appropriate to revise Eq (1) byEq (2) adopting only the attractive forces from upstream nodes,which are more robust against network topology change and

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more accurate when the robots are turning around corners.

− �∇f |p0 =∑

f(pi)<f(p0)−−→p0pi (2)

2) Collision problem, deviation problem and their solu-tions: Caused by the error in the reversed gradient estimation,frequently the robot collides with obstacles and occasionallythe robot deviates from the planned path, as demonstratedby our experiments. The collision, or intrusion into the hightemperature region in Fig. 6(a), may paralyze the functionof robots and endanger the overall task completion. Thedeviation, like in Fig. 6(b), not just wastes robot’s energybut also may lead the robot out of the deployment region,where it’s impossible for the robot to seek guidance from staticsensors. The possibility of moving out of navigation field ismuch higher for the navigation band based algorithm, in whichonly sensors along the planned path can provide guidance. Wename this problem as the “out-of-field” problem. However, it isdifficult to qualify the possibilities of the two exceptional cases- collision and out-of-field, mainly because of the difficulty inquantifying the error in the reversed gradient estimation.

Escape from the fire

Intrusion into impassble region

(a) Detect a collision then escape.

Stray away

Return back

NormalCourse

(b) Stray away then return back.

Fig. 6. Enhance the robustness of navigation to collision and straying away.

We solve the collision problem by exploiting the agilereadings from the robot self-carried sensors, which belongsto the Local Obstacle Avoidance layer in Fig. 1. This solutionneeds two devices on a robot: a temperature sensor and a heatsource detector with only coarse precision. As indicated bythe Escape rule in TABLE IV, the robot detects the collisionby comparing current temperature reading with a predefinedalert threshold. If it’s higher than the alert threshold, theEscape rule constructs a repulsive force to avoid the collision.The direction of the repulsive force escaping from the fire isretrieved from the heat source detector and its magnitude isthe adjustable escaping step size. The Fig. 6(a) illustrates theworking of the Escape rule with alert threshold is set to 100degree and escaping step configured to 10. The robot detectsthe collision happened by finding its temperature reading isabove 100 degree. Then it moves out of the impassable regionfollowing the direction away from the fire and with step size10. After the evacuation, the robot reissues the request forguidance within its neighborhood and continues its mission.Although in Fig. 6(a) the collision actually happens, potentialcollision can be avoided by changing the behavior patternfrom collide-then-escape to predict-collision-then-escape. The

TABLE IVADDING THE ESCAPE RULE

defrule Escape :

sensed temperature is above the alert threshold ⇒construct a vector �e escaping from the fire detected by a coarse

heat source detector;

force := �e/|�e| · escaping step size.

collision prediction can be implemented in our scenario byconfiguring an alert threshold lower than the temperaturethreshold of impassable region, like 80 degree. The assumedavailableness of temperature reading and heat source informa-tion to robots can be abstracted as the robots’ local obstacleavoidance abilities. The assumption of this ability is also validin other scenarios, e.g. the wall is the obstacle and the robothas the ultrasound based obstacle sensing ability.

We mitigate the out-of-field problem by expanding thenarrow navigation band along planned path to the broad DH-APF based navigation field covering the entire deploymentregion. Therefore, in Fig. 6(b), even when the robot straysaway to the right bottom corner, far away from the the plannedroute. Still, it can retrieve the reversed field gradient fromsurrounding and get back to normal course later. We admit thatwith our solution it is still possible for the occurrence of out-of-field event, e.g. the robot again makes wrong decision aboutnext step moving direction at the right bottom corner. Actually,we doubt the existence of an ultimate solution that robotsnever get lost. At least, our solution gives the sensor networkdeployer a method to reduce the out-of-field possibility bythrowing more sensors and broaden the deployment region.

3) Motion oscillation problem and its solutions: Anotheradvantage of replacing the navigation bands by our DH-APFbased navigation fields is to mitigate the oscillation problemin narrow passages. We observe that when the robot movesin narrow corridors, it often encounters a path oscillationproblem, as illustrated by Fig. 7. When the robot locates nearthe center of the corridor, it tends to move by a smoothedtrajectory, represented by a blue line in graph. However, whenthere is a disturbance that the robot locates near the boundaryof the corridor, its moving path oscillates along the bluesmoothed path. In fact, [5] naturally creates such a corridorby building a navigation band along the planned path and theoscillation in robots’ motion can be anticipated. The existenceof oscillation problem get verified by our experiment inFig. 8(a). Here, the initial disturbance required by oscillationsis introduced by making the robot to turn around a corner.

EventPoint

Robot

Robot

Oscillated PathSmoothed Path

Roughly Equal Areas

Ideal Navigational Band Built from Concentric Rings

Fig. 7. Model of oscillations in a narrow passage or a navigational band.

The oscillation problem in fact is inevitable for artificialpotential field based methods as argued by [6]. We however

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can mitigate it here by throwing more sensors and expandingthe corridors. In Fig. 8(b), with the two layers at the topwhich provides additional attractive forces, the motion of therobot no longer oscillates. It turns around the corner smoothly,which shortens the time to arrive at the target. Another cheapermitigation than the corridor expansion is reducing the step sizewhen detecting a dramatic change in the sequence of reversedgradient estimates. When there is only slight changes in thegradient estimates sequence, we can enlarge the step size toreduce the interactions between robots and static sensors, thussave the precious energies of static sensors and increase therobots’ moving speed. A thorough investigation into the energyfeatures of this dynamic step size scheme is our future works.

Robot begins to oscillate at this point

(a) Unstable motions in narrow cor-ridors.

The robot would turn downwards at this point, if without the two upper layers of sensors. Then it would suffer from oscillations.

(b) Stable motions in broad re-gions.

Fig. 8. Oscillation in narrow passages and a possible mitigation.

4) Conclusion: The robot navigation guided by networkedstatic sensors is unreliable, which requires careful engineeringefforts. This unreliability mainly originates from the irreg-ular, fault-prone nature of wireless communication and canbe worsen by sparse and nonuniform sensor distributions.Our proposed solutions here are to increase robot navigationreliability by exploiting robot self-carried sensors to granteethe collision-free property, and by throwing more sensors tocover a broader region to mitigate the out-of-field problemand the path oscillation problem, especially when the robotturns around the corners. With these efforts on navigationreliability, it’s possible for our algorithm to configure a largestep size, which reduces the interactions with static sensors,saves sensors’ energies and increases the speed of robots.This large step size is impossible for other robot navigationalgorithms, since the large step size increases the possibility ofout-of-band, oscillation and collision, which can not be wellhandled by them.

VI. SIMULATIONS

A. Experiment Setup

We setup our simulation platform as described below. Thepath planning algorithm in TABLE I&II is developed bynesC over TinyOS [11]. The robot navigation algorithm inTABLE III&IV is implemented by a mixture of nesC andTython scripts [12]. We simulate the unreliable radio linksby TOSSIM’s empirical bit error model [13]. The sensors areplaced either in regular grids or in disturbed grids. Althoughthe grid spacing is fixed throughout our experiments, we stillhave control over the network density or the average node

degree by adjusting the radio transmission range. Obstacles inthe sensor deployment region can be simulated by one of thetwo ways: (1) turn off motes in the obstacle regions; (2) createa Tython SimObject with a high temperature attribute.

We use the follow notations for our experiments:D : sensor distribution density 100

100·100ft2= 0.01sensor/ft2

R : average symmetric communication range ≈ 20ftk : range scaling factorr : average symmetric communication range R

kd : average node degree in the symmetric topology πr2D

B. Experiment on Trajectory Smoothness

Let lt be the length of robot trajectory generated by ourreliable robot navigation algorithm and lr be the length of areversed routing path. Our experiments, by comparing lt withlr, are to demonstrate our algorithm can produce smoothertrajectories than the shortest routing path and it’s safer tofunction in twisted corridors environments. The reason why wechoose the shortest routing path for comparison is that manyalgorithms are proposed to steer the robot along it, though theymay not actually achieve the same efficiency with routing path.

In Fig. 9∼12, robot trajectories are represented by redpolylines, while shortest routing paths are represented by bluedotted polylines. The red robot trajectories do not need toend precisely at the event owner, since the robot stop itsengine once it arrives within the one hop range of the eventowner. Our algorithm has been tested in various network con-figurations. The primary network parameter we varied is theradio range r by adjusting the scaling factor k. The functionalrelation between r and k can be found in Subsection VI-A.Other factors include the sensor distribution pattern (regulargrid topology or disturbed grid topology) and deploymentregion (with or without obstacles). In experiments, the functionadopted to estimate the reversed field gradients is Eq. (2).

(a) k = 1, d = 12.56. (b) k = 1.15, d = 10.9. (c) k = 1.3, d = 7.44.

Fig. 9. A comparison in rectangular fields with disturbed grid placement.

(a) k=1, d=12.56. (b) k=1.15, d=10.9. (c) k=1.3, d=7.44.

Fig. 10. A comparison in rectangular fields with disturbed grid placement.

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In Fig. 9, the length of multihop routing paths in a regulargrid topology is sensitive to the change in sensor density.However, no obvious variations can be witnessed for the lengthof red trajectories generated by our algorithm. Comparedwith the shortest routing paths, our trajectories are constantlyshorter and more smoothed. This advantage originates fromEq. (2), because in the routing path, only one node is chosenfrom a pack of upstream sensors as the next hop node,and however, in our robot trajectory, the next step movingdirection is determined by “averaging” the attractive forces byall upstream sensors. This advantage can also be witnessedin disturbed grid topologies in Fig. 10, i.e., although therouting paths become smoother in disturbed grid topologiesthan in regular grid topologies, our trajectories still exhibitbetter quality. Another observation from Fig. 9&10 is that ourtrajectories is not sensitive to the change in network densities.This is probably due to the small amount of data exchangesrequired by our algorithm. Therefore, a denser network withsymmetric node degree 12.56 does not necessarily mean muchheavier message loss (due to radio conflicts), and a sparsenetwork with symmetric node degree 7.44 is sufficient for therobot to make a good decision about the next step movingdirections.

Fig. 11&12 make similar comparisons in twisted corridors.The shortest routing paths have very short moving distance,which are confined by the corridors and are prone to stickto the corners when turning around them. As a comparison,robots applying our algorithm tend to keep a descent distanceaway from the obstacles, since the lower-hop-count upstreamnodes that do not stick to obstacles also exert their attractiveforces over the robot. Therefore, though our trajectories are alittle longer than the routing paths in twisted corridors, theyprovide higher safety.

(a) k=1, d=12.56. (b) k=1.15, d=10.9. (c) k=1.3, d=7.44.

Fig. 11. A comparison in twisted corridors with regular grid placement.

(a) k=1, d=12.56. (b) k=1.15, d=10.9. (c) k=1.3, d=7.44.

Fig. 12. A comparison in twisted corridors with disturbed grid placement.

VII. CONCLUSION

The algorithm presented in this paper provides a solutionto guide a mobile sensor to the region of phenomenon in areliable way. This reliability is achieved by (1) avoiding thelocal trap by exploiting a global DH-APF; (2) solving theproblem of deviation from a planned global path; (3) avoidingcollision with obstacles; (4) mitigating the motion oscillationproblem. Though the proposed algorithm cannot ensure perfecttoleration of navigation path deviation and oscillation, it givesinsight as how to use the DH-APF to reduce the possibilityof out-of-field problem and improve the navigation trajectoryefficiency. Besides the reliability features, this algorithm is alsoenergy-efficient in the sense of (1) saving the energy of staticsensors by reducing the interaction between robot and them;(2) saving the energy of robot by constructing a smoothedtrajectory shorter than or at least comparable to the shortestrouting path. The analysis and experiments in the paper are ofa high fidelity, which consider practical issues of error-pronewireless commutations with implementations on TinyOS.

ACKNOWLEDGMENT

This work was supported in part by HK RGC PolyU5322/08E.

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